This book presents a broad exposition of analytical and numerical methods for modeling composite materials, laminates, polycrystals and other heterogeneous solids, with emphasis on connections between material properties and responses on several length scales, ranging from the nano and microscales to the macroscale.
Many new results and methods developed by the authorare incorporated into the rich fabric of the subject,which has developed fromthe work of manyresearchersover the last 50 years. Among the new results, the book offers an extensive analysis of internal and interface stresses caused by eigenstrains, such as thermal, transformation and inelastic strains in the constituents, which often exceed those caused by mechanical loads, and of inelastic behavior of metal matrix composites. Fiber prestress in laminates, and modeling of functionally graded materials are also analyzed. Furthermore, this bookoutlines several key subjects on modeling the properties of composites reinforced by particles of various shapes, aligned fibers, symmetric laminated plates and metal matrix composites.
This volumeis intended for advanced undergraduate and graduate students, researchers and engineers interested and involved in analysis and design of composite structures.
Table of Contents
1 Tensor component and matrix notation.- 2 Anisotropic elastic solids.- 2.1 Elastic strain energy density.- 2.2 Material symmetries.- 2.3 Transversely isotropic composite materials.- 2.4 Cylindrically orthotropic materials.- 2.5 Young’s modulus, shear modulus and Poisson’s ratio.- 3 Elementary concepts and tools.- 3.1 Aggregates and constituent phases.- 3.2 Herogeneous microstructures.- 3.3 Representative volume.- 3.4 Local and overall stress and strain fields.- 3.5 Overall properties and local fields.- 3.6 Transformation fields.- 3.7 Work, energy and reciprocal theorems.- 3.8 The Levin formula and the Hill lemma.- 3.9 Universal connections for elastic moduli of fibrous composites.- 3.10 Constitutive relations and local fields in heterogeneous aggregates.- 4 Inclusions, inhomogeneities and cavities.- 4.1 Homogeneous ellipsoidal inclusions: The Eshelby solution.- 4.2 Ellipsoidal inhomogeneities: The equivalent inclusion method.- 4.3 Transformed inhomogeneities.- 4.4 Dilute approximation of overall properties.- 4.5 Green's function and Eshelby's tensor in elastic solids.- 4.6 Coefficients of the P tensors for selected ellipsoidal shapes.- 4.7 Summary of principal results.- 5 Energies of inhomogeneities, dilute reinforcements and cracks.- 5.1 Energy changes caused by mechanical loads.- 5.2 Energy changes caused by uniform phase eigenstrains.- 5.3 Energy changes caused by mechanical loads and phase eigenstrains.- 5.4 Energy and stiffness changes caused by cracks.- 6 Evaluations and bounds on elastic moduli of heterogeneous materials.- 6.1 Elementary energy bounds.- 6.2 Hashin-Shtrikman and Walpole bounds on overall elastic moduli.- 6.3 Evaluation of H-S bounds for ellipsoidal inhomogeneities.- 6.4. Composite element assemblage bounds.- 6.5 The generalized self-consistent method.- 7 Estimates of mechanical properties of composite materials.- 7.1 The self-consistent method (SCM).- 7.2 The Mori-Tanaka method (M-T).- 7.3 The differential scheme.- 7.4 The double inclusion and double inhomogeneity models.- 7.5 Applications of SCM and M-T to functionally graded materials.- 8 Transformation fields.- 8.1 Uniform change of temperature in two-phase composites and polycrystals.- 8.2 Transformation influence functions and concentration factors.- 8.3 Uniform change in temperature in multiphase systems.- 8.4 Capabilities of bounds and estimates of overall and local fields.- 9 Interfaces and interphases.- 9.1 Perfectly bonded interfaces.- 9.2 Imperfectly bonded inhomogeneities and cavities.- 10 Symmetric laminates.- 10.1 Constitutive relations of fibrous plies.- 10.2 Coordinate systems and transformations.- 10.3 Overall response and ply stresses in symmetric laminates.- 10.4 Ply and constituent stress and strain averages .- 10.5 Design of laminates for cylindrical pressure vessels.- 10.6 Dimensionally stable laminates.- 10.7 Auxetic laminates.- 10.8 Laminates with reduced free edge stresses.- 11 Elastic-plastic solids.- 11.1 Yield and loading surfaces, normality and convex.- 11.2 Hardening and flow rules.- 11.3 Matrix form and consistency of the instantaneous tangent stiffness.- 12 Inelastic composite materials.- 12.1 Transformation field analysis (TFA) of inelastic deformation.- 12.2 Experimental support of theoretical predictions.- 12.3 Thermal hardening.- References.